-LRB- CNN -RRB- -- The images of Haitian children crying or injured or wandering the streets alone are heartbreaking . It 's no surprise there has been a flood of well-intentioned people who want to adopt those children .

But that 's not always the best immediate move , aid groups caution .

Save the Children Chief Executive Jasmine Whitbread said the `` vast majority '' of children on their own in Haiti are not orphans , but were simply separated from their families in the chaos .

Their family members may still be alive , she said , and `` will be desperate to be reunited with them . ''

`` Taking children out of the country would permanently separate thousands of children from their families -- a separation that would compound the acute trauma they are already suffering and inflict long-term damage on their chances of recovery , '' Whitbread said .

Hurriedly whisking unclassified children out of Haiti will not ensure the children are happy or safe in the long-term , experts said . Homes and potential parents must be reviewed by professional social workers and it 's logistically impossible to do that in a short time . Allowing adoptions to proceed without thorough background checks can lead to child trafficking and other crimes .

The United Nations Children 's Fund , or UNICEF , does not facilitate adoptions , but it has been bombarded with calls from people who want a Haitian orphan , said Christopher de Bono , a UNICEF spokesman .

In 2007 , UNICEF estimated that there were 380,000 orphans in Haiti , but de Bono said Thursday that he 'd `` hate to vouch for that figure '' because that number -- any number -- is impossible to verify .

Between Haiti 's `` lousy -LSB- child welfare -RSB- oversight system , '' and all the challenges that Haitians have endured , it 's not uncommon for Haitian parents to put their children in orphanages temporarily , de Bono said . This means knowing who is truly an orphan and who is n't requires great attention to detail and documents .

`` Removing children who 've just experienced a disaster from their environment , from where they 're from is not necessarily good for them , '' he said . Haitian children must first be fed , sheltered , clothed and given medical attention ; the next step is to register them and trace their relatives .

Diana Boni , who works with Port-au-Prince 's BRESMA orphanage , is firmly against new adoptions out of Haiti . `` Under no circumstances should we evacuate any child newly orphaned or displaced , '' she wrote in an e-mail to CNN .

`` Imagine losing much of your family , only to discover that a surviving relative had been whisked off to the States to be adopted by strangers without your knowledge or consent ! Adoptions without consent are child trafficking . Pure and simple . ''

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She has been taking care of children who waited for years in the orphanage to be adopted . `` It 's a bit sad , as I have several wonderful children who waited literally for years for new families , and no one ever came , '' she said .

The disaster in Haiti has led to an outpouring of support around the world , with the United States alone donating more than $ 305 million as of Wednesday , according to the Chronicle of Philanthropy , a newspaper covering nonprofit organizations .

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Because Haiti 's poverty already made it `` extremely vulnerable '' to exploitation and abuse , rushed adoptions could open the door to traffickers , said World Vision Chief Executive Justin Byworth .

`` We are concerned not only about premature overseas adoption but also about children increasingly being sent unaccompanied to the Dominican Republic , '' he said .

Aid groups said adoptions that were already in progress before the January 12 earthquake should go ahead , as long as the right legal documents are in place and they meet Haitian and international law .

For those who want to help Haitian children , Whitbread said , they should donate to aid agencies that are working on reuniting children with their families .

The International Committee of the Red Cross has opened an office at the headquarters of the Haitian Red Cross in Crois de Prez to help people locate their relatives , said Pete Garratt , a disaster response manager at the British Red Cross .

The Red Cross also has set up a Web site to help people searching for relatives , he said .

CNN 's Jessica Ravitz contributed to this report .

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Experts : Hurried adoptions can lead to trafficking and cause more trauma to children

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Aid groups say focus should be on reuniting kids with relatives

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Reports on plight of children in Haiti has led many to ask about adoptions